PROBLEMS OF UNIVERSITY ENTRANCE EXAMINATION OF BUSINESS ECONOMICS 29/78

3rd PART - TOPIC 9.- (You must do mainly those in bold)

PR_2.01_03.- The firm MEGA, Ltd. is studying three investments. The initial outlay and the cash flows of each investment in euros appear in the table. Determine which one would be the best investment to the firm according to the criteria of the Net Present Value or NPV. Consider an annual interest rate of 7%. OUTCOMES: NPVX = 12,088.13€, NPVY = 9,364.74€, NPVZ = 3,985.75€ SOL_PR_2.01_03

 Project Initial outlay Q1 Q2 Q3 Q4 X 18,000 7,000 9,000 8,000 12,000 Y 30,000 15,000 15,000 15,000 ----------- Z 25,000 12,000 11,000 10,000 -----------

PR_2.02_03.- The firm WERBEL sells bicycles and it's thinking about the possibility of expanding its business towards the sale of clothes and complements used to do cycling. In order to that it has planned an outlay of 600,000 ptas. and the following collections and payments. Determine if the investment is interesting to the firm OUTCOMES: PB = xy, 8 m and 28 d. NPV = -74,393.68€ SOL_PR_2.02_03

 YEARS COLLECTIONS PAYMENTS 1 100,000 50,000 2 200,000 60,000 3 300,000 65,000 4 300,000 65,000

1. According to the criteria of the Payback, knowing that the minimum demanded period of time is five years

2. According to the criteria of the Net Present Value, if the interest rate is 8%

PR_2.03_03.- The Manufactures of the Bay's manager wants to improve the productivity of his firm, therefore, he wants to know the firm's cash conversion cycle before of the beginning of the program of improving. Calculate the information that the manager needs related to the cash conversion cycle if the data are the following (averages of the period and in million of pesetas): OUTCOMES: RMp = 23.53 days, GPp = 8.33 days, FGp = 20.86 days, Rp = 20.86 days, CCC = 73.58 days SOL_PR_2.03_03

 ITEMS AMOUNTS Sales cost 2,012 Total cost of production 2,104 Average raw material stock 63 Average finished goods stock 115 Material purchases 977 Total sales 2,415 Average goods in process stock 48 Average receivables stock 138

PR_2.04_03.- Determine the more profitable choice to an investor who is offered the following possibilities to make a certain investment, according to the criteria of the Net Preset Value (NPV) if the interest rate is 7%: OUTCOMES: NPVA = - 207,647€; NPVB = - 103,697; NPVC = 185,716€ SOL_PR_2.04_03

 Initial Outlay Net Cash Flow 1st Year Net Cash Flow 2nd Year Net Cash Flow 3rd Year Net Cash Flow 4th Year Net Cash Flow 5th Year Project A 1,000,000 100,000 150,000 200,000 250,000 300,000 Project B 1,500,000 200,000 300,000 350,000 400,000 500,000 Project C 1,700,000 400,000 600,000 300,000 600,000 400,000

PR­_2.05_03.- The data related to three projects of investment that a firm wants to evaluate are in the attached table. If the interest rate is 6%: OUTCOMES: NPVA = 5,768,343.06€; NPVB = 1,318,898.21€; NPVC = 3,558,576.88€, PBA = x y and 8 m, PBB = x y and 3 m, PBC = x y, 10 m and 15 d SOL_PR_2.05_03

1. Put in order the aforementioned investments according to their order of preference

1. By usin the criteria of Net Present Value (NPV)

2. By using the criteria of Payback

2. Comment the outcome

 Projects Initial Outlay Net Cash Flow 1st Year Net Cash Flow 2nd Year Net Cash Flow 3rd Year Net Cash Flow 4th Year Net Cash Flow 5th Year A 10,000,000 0 0 6,000,000 6,000,000 8,000,000 B 20,000,000 3,000,000 4,000,000 5,000,000 6,000,000 8,000,000 C 16,000,000 4,000,000 5,000,000 8,000,000 3,000,000 3,000,000

PR_2.06_03.- If the annual interest rate is 8%: OUTCOMES: NPVA = 3,829,086.43; NPVB = -3,524,416.59; NPVC = 2,587,894.88; PBA = x y and 10 m, PBB = x y and 9 m, PBC = x y, 10 m and 15 d SOL_PR_2.06_03

1. Put in order the investments according to the order of preference

1. By using the criteria of Net Present Value (NPV)

2. By using the criteria of Payback

 Initial Outlay Net Cash Flow 1st Year Net Cash Flow 2nd Year Net Cash Flow 3rd Year Net Cash Flow 4th Year Net Cash Flow 5th Year project A 10,000,000 1,000,000 -2,000,000 6,000,000 6,000,000 8,000,000 project B 18,000,000 -3,000,000 4,000,000 5,000,000 6,000,000 8,000,000 project C 16,000,000 4,000,000 5,000,000 8,000,000 3,000,000 3,000,000

PR_2.07_03.- We want to know which of the following two investments is preferable according to the Payback and to the Net Present Value (NPV). The annual interes rate is 10%. Is there an agreement between both criteria? Comment the outcomes and reason the answer OUTCOMES: PBA = x y; PBB = x y; NPVA = 5,849.50; NPVB = 11,789.50 SOL_PR_2.07_03

 Investment A Investment B Initial outlay 10,000 10,000 1st Cash Flow 5,000 2,000 2nd Cash Flow 5,000 4,000 3rd Cash Flow 5,000 4,000 4th Cash Flow 5,000 20,000

PR_2.08_03.- The firm PLAVAN Ltd. is thinking about two possible projects of investment. Determine the Payback and the Net Present Value of each one of the investments. The annual interest rate is 10%. Is there an agreement between both criteria in order to establish which one is the best option to the firm? Reason your answer OUTCOMES: NPVA = 2,787.37; NPVB = 1,113.44; PBA = x y and 3 m; PBB = x y SOL_PR_2.08_03

 Initial outlay Cash Flow 1st Year Cash Flow 2nd Year Cash Flow 3rd Year Project A 10,000 2,000 6,000 8,000 Project B 8,000 3,000 5,000 3,000

PR_2.09_03.- The corporation QQQ has a Share Capital of 73,647€ divided in 4,900 shares. The shares of the aforementioned corporation quote in the Stock Market at 165% and the expected annual dividends are 2.40€. The annual interes rate is 7%. Calculate the nominal value, the market value and the theoretical value of the shares of the corporation QQQ OUTCOMES: NV = 15.03 €/share; MV = 24.80 €/share; TV = 34.29 €/share SOL_PR_2.09_03

PR_2.10_03.- PERFUMASA is planning to make a new investment, in order to that, it has several options: either to diversify towards another line of products or to expand the existing line. The data for the study of the profitability of the investment appear in the following table (in euros). Help you to decide which investment would you prefer and why according to the criteria of Net Present Value and Payback. The annual interest rate is 7%. OUTCOMES: NPVD = -15,430.37, NPVE = 79,458.96, PBD = x y, PBE = x y, 3 m and 18 d SOL_PR_2.10_03

 Initial outlay Collectins 1st Year Payments 1st year Collections 2nd Year Payments 2nd Year Collections 3rd Year Payments 3rd Year Diversification 90,000 50,000 60,000 140,000 100,000 150,000 90,000 Expansion 78,000 180,000 120,000 180,000 120,000 180,000 120,000

PR_2.11_03.- A project of investment had an initial outlay of 100,000€ and the cash flows of the first and second years were 40,000 and 30,000€, respectively. Calculate the cash flow of the third year, if the Payback of the investment was 2 years and 9 months OUTCOME: x = 40,000€ SOL_PR_2.11_03

PR_2.12_03.- A building firm with 120,000€ of Share Capital made up of 300 shares, has obtained a distributing profit of 12,000€ at the end of the year and it has created reserves of 24,000€. Determine: OUTCOMES: NV = 400€; TV = 480€; DIV = 40€; Net worth = 144,000€ SOL_PR_2.12_03

1. The nominal value of the shares

2. The theoretical value of each share

3. The distributed dividend per share

4. The Net worth

PR_2.13_03.- Obtain the Net Present Value of an investment with an useful life of 5 years, which initial outlay is 1,500 m.u. that are paid in only one time and that have the following collections and payments (in m.u.). The annual interest rate is 5%. OUTCOME: NPV = 292.85 m.u. SOL_PR_2.13_03

 YEARS COLLECTIONS PAYMENTS 1 600 300 2 700 400 3 1,000 500 4 1,000 500 5 1,000 500

PR_2.14_03.- You have the data in monetary units related to three projects of investment that a firm wants to evaluate in the attached table. If the annual interest rate is 6.5%. OUTCOMES: NPVA = 9,163.35€; NPVB = -2,380.57€; NPVC = 5,998.32€; PBA = x y and 10 m, PBB = x y, 9 m and 18 d, PBC = x y, 8 m and 17 d SOL_PR_2.14_03

1. Put in order of preference the investments by using the criteria of Net Present Value (NPV)

2. Put in order of preference the investments by using the criteria of Payback,

 INITIAL OUTLAY NET CASH FLOWS 1st Year 2nd Year 3rd Year 4th Year PROJECT A 25,000 0 0 30,000 12,000 PROJECT B 20,000 -5,000 -2,000 15,000 15,000 PROJECT C 16,000 5,000 6,000 7,000 8,000

PR_2.15_03.- A firm is studying two projects of investment; A and B. Project A means an initial outlay of one million of euros and it's expected to obtain, each one of the five years that it will last, a net cash flow of 300,000€. Project B means an initial outlay of one million euros, as well, but the net cash flows are: 150,000€ 1st year, 250,000€ 2nd year, 450,000 3rd year, 400,000 4th year and 350,000 5th year. If the annual interest rate is 5%, determine which investment is the best, by evaluating them using the NPV method. OUTCOMES: NPVA = 298,843€ and NPVB = 361,656.58€ SOL_PR_2.15_03

PR_2.16_03.- WE'VE GOT ANOTHER PROBLEM LIKE THIS ONE

PR_2.17_03.- It's equal to 2.12_03 SOL_PR_2.17_03

PR_2.18_03.- An investment is offered the two following possibilities to make a certain project. Determine the more profitable option, according to the criteria of Net Present Value (NPV) if the interest rate is 8% and according to the Payback. OUTCOMES: NPVA = 691.6€; NPVB = - 1,620.17€; PBA = x y and 10 m; PBB = x y and 6 m SOL_PR_2.18_03

 PROJECT A PROJECT B Collections € Payments € Collections € Payments € Initial outlay 10,000 Initial outlay 14,100 1st year 4,000 2,000 1st year 6,000 3,000 2nd year 5,000 2,500 2nd year 6,800 3,400 3rd year 8,000 5,000 3rd year 8,200 5,000 4th year 6,000 3,000 4th year 7,000 4,000 5th year 5,600 2,500 5th year 8,000 5,000

PR_2.19_03.- The firm “Babe Apples” markets apple trees to nurseries. Its Share Capital is divided in 50,000 shares of 1,000 m.u. each one. The firm quotes in the Stock Market at 1,256 m.u./share and it has reserves of 10,000,000 m.u. OUTCOMES: SC = 50,000,000 m.u.; QUOTE . . . PAR, TV = 1,200 m.u. SOL_PR_2.19_03

1. Calculate the amount of the Share Capital

2. Determine if the shares quote under par, over par or at par

3. Calculate the theoretical value of each share

PR_2.01_04.- A firm has the following information about two projects of investment. a) Which of the two investments is preferable according to the criteria of Payback? and b) Which investment is more profitable? Comment the outcome. OUTCOMES: PB1 = x y and 10 m; PB2 = x y and 14 d SOL_PR_2.01_04

 Investment 1 Investment 2 Initial outlay 1,500 1,500 Cash flow of the 1st period 1,000 100 Cash flow of the 2nd period 600 1,000 Cash flow of the 3rd period 0 10,000

PR_2.02_04.- A firm plans to make a project of investment to acquire a machine valued in 13,000€. The project lasts four years. The planned revenue for each year with the acquisition of this new machine are: 6,000€; 12,000€; 12,500€ and 20,000€ respectively. The planned operating expenses appear in the following table. The interes rate is 15%; the salvage value is zero and the tax on profits is 25%. You must decide if the investment is a good idea for the firm or not, according to the Net Present Value (NPV). OUTCOME: NPV = 9,888.6€ SOL_PR_2.02_04

 EXPENSES 1st year 2nd year 3rd year 4th year Labour 600 630 750 800 Raw material 300 300 400 400 General expenses 150 200 200 150

PR_2.03_04.- A firm is thinking about to acquire a machine with an useful life of 4 years. The investment means to pay initially 3,000€ and 1,000€ each one of the years, the planned collections are 2,000€ each year. If the salvage value of the machine is 200€ and the interest rate is 5%. Calculate the NPV of the investment. OUTCOME: NPV = 710.49€ SOL_PR_2.03_04

PR_2.01_05.- A firm has two alternative projects of investment. Calculate the NPV, knowing that the interest rate is 4%, and reason which investment would interest to make. RESULTADOS: VANX = 16.605,83, VANY = 16.750,9 SOL_PR_2.01_05

 Project Initial outlay 1st year 2nd year 3rd year Collections Payments Collections Payments Collections Payments X 11,000 12,000 4,000 15,000 5,000 18,000 6,000 Y 11,000 15,000 5,000 17,000 7,000 20,000 10,000

PR_2.02_05.- If we have the projects of investment that appear in the attached table, and, if the annual interest rate is 8%: OUTCOMES: NPVA = 427.78 m.u.; NPVB = 308.39 m.u.; NPVC = -759.79 m.u.; PBA = x y, 8 m and 10 d; PBB = x y and 6 m; PBC = x y and 8 m SOL_PR_2.02_05

 Projects Initial outlay (m.u.) Net Cash Flow 1st year (m.u.) Net Cash Flow 2nd year (m.u.) Net Cash Flow 3rd year (m.u.) A 10,000 7,500 3,600 500 B 10,000 4,000 4,000 4,000 C 10,000 0 8,000 3,000

1. Indicate which is the best project of investment according to the Net Present Value (NPV)

2. Calculate the Payback of each one of these projects, considering that the cash flows are obtained in an uniform way along the year. According to this criteria, which project will be the best to the firm?

PR_2.03_05.- A firm has the chance of invest in one of these three projects: OUTCOMES: PB1 = x y and 8 m; PB2 = x y, 8 m and 23 d; PB3 = x y, 8 m and 22 d, NPV1 = 5,219.85€; NPV2 = 5,328.19€; NPV3 = 6,473.82€ SOL_PR_2.03_05

 Projects Initial outlay Net Cash flows 1st year 2nd year 3rd year P1 80,000 ------- 50,000 45,000 P2 90,000 52,000 ------- 52,000 P3 80,000 40,000 --------- 55,000

1. According to the Payback, which is the best investment? Consider that the cash flows are obtained in an uniform way along the year

2. According to the Net Present Value (NPV), which is the best investment, if the annual interest rate is 4.5%?

PR_2.04_05.- A firm's chief financial officer asks for your collaboration to evaluate the advisability of each one of the three projects of investment that appear in the following table. According to the chief officer, project A is the best option for the firm. Calculate the Payback of each investment and indicate if your opinion is the same as the chief financial officer. Consider that the net cash flows are obtained in an uniform way along the year. OUTCOMES: PBA = x y, 7 m and 15 d; PBB = x y, 11 m and 12 d; PBC = x y, 11 m and 4 d SOL_PR_2.04_05

 PROJECTS INITIAL OUTLAY NET CASH FLOWS 1st year 2nd year 3rd year 4th year A 18,000 6,000 7,000 8,000 9,000 B 15,000 -3,000 -1,000 0 20,000 C 13,000 0 0 14,000 10,000

PR_2.05_05.- A firm has three choices of investment, that mean an initial outlay and ones net cash flows that appear in the following table. If we suposse an annual interest rate of 4%, put in order from the highest to the lower profitability these investments, by using the criteria of: OUTCOMES: NPVA = 18,210.98; NPVB = 11,558.26; NPVC = 8,880.32; PBA = x y, 1 m and 6 d; PBB = x y and 23 d; PBC = x y and 3 m SOL_PR_2.05_05

 Projects of investment Initial outlay Net cash flows 1st year 2nd year 3rd year 4th year Investment A 20,000 10,000 8,000 20,000 4,000 Investment B 27,000 8,000 18,000 16,000 0 Investment C 8,000 6,000 -1,000 12,000 1,600

1. Net Present Value (NPV)

2. Payback, considering that the cash flows are obtained in an uniform way along the year

PR_2.06_05.- Investments A and B have the following characteristics: OUTCOMES: PBA = x y, 9 m and 18 d; PBB = x y and 3 m; NPVA = 194.32; NPVB = 11,295.78 SOL_PR_2.06_05

 Investment A Investment B Initial outlay 10,000 10,000 Net cash flow of the 1st period 6,000 1,000 Net Cash Flow of the 2nd period 5,000 4,000 Net Cash Flow of the 3rd period 100 20,000

1. According to the Payback, which investment is preferable? Calculate the payback of both investments considering that the cash flows are obtained in an uniform way along the year

2. According to the NPV, which investment is preferable? (consider an interest rate of 6%) Explain the differences with the outcomes of point a)

PR_2.01_06.- The firm OO's chief financial officer, is studying the posibility of expanding the factory, in order to that, three projects have been presented. The temporal analysis of these investments is in the following (data in million of m.u.): OUTCOMES: NPVA = -15.19; NPVB = 81.1; NPVC = -83.2; PBA = x y, 2 m and 20 d; PBB = x y; PBC = x y SOL_PR_2.01_06

NET CASH FLOWS OF THE PERIODS

 Projects Initial outlays 1st year Q1 2nd year Q2 3rd year Q3 4th year Q4 5th year Q5 A 800 -50 150 250 350 450 B 950 100 200 300 350 500 C 750 -50 100 400 300 200

The interest rate is 10%. Considering that the net cash flows are maintained uniform along the year.

Obtain the classification of the projects according to the criteria of Payback and NPV

PR_2.02_06.- A firm has the possibility of investing in one of these three projects: OUTCOMES: NPV1 = 2,913.29; NPV2 = 627.36; NPV3 = 13,868.91; PB1 = x y, 9 m and 18 d; PB2 = x y, 8 m and 17 d; PB3 = x y, 7 m and 15 d SOL_PR_2.02_06

 Net cash flows Projects Initial outlay 1st year 2nd year 3rd year P1 180,000 ----- 100,000 100,000 P2 190,000 70,000 70,000 70,000 P3 160,000 110,000 ---- 80,000

a. Which one do you choose according to the criteria of Payback? Considering that the cash flows are obtained in an uniform way along the year.

b. Which one do you choose according to the criteria of net present value, NPV, if the interest rate is 5%?

PR_2.03_06.- A project of investment presents the following data: initial outlay of 1,500 m.u.; annual interest rate 6% and: OUTCOMES: NPV = 239.51; PB = x y, 9 m and 18 d SOL_PR_2.03_06

 YEARS COLLECTIONS PAYMENTS 1 600 300 2 700 400 3 1,000 500 4 1,000 500 5 1,000 500

Calculate the NPV and the Payback of the project

PR_2.04_06.- Given the following projects of investment: OUTCOMES: NPV1 = 312.6; NPV2 = 98.8; PB1 = x y and 8 m; PB2 = x y and 10 m SOL_PR_2.04_06

 PROJECT 1 PROJECT 2 INITIAL OUTLAY  5,000 5,000 NET CASH FLOWS 1st year ---- 1,000 2nd year 3,000 ---- 3rd year 3,000 4,800

Calculate: If we suposse that the net cash flows are obtained in an uniform way along the year.

1. Which project of investment is preferable according to the Payback?

2. Given an annual interest rate of 5%. Which project would you choose according to the NPV or net present value?

PR_2.05_06.- The firm “Ciclomasa” dedicates itself to the sale of sport machines and it's thinking about the possibility of expand its business towards the sale of clothes and complements used to the sport. In order to that, it has planned an initial outlay of 600,000€ and the following net cash flows: OUTCOMES: NPV = 246,663.3; PB = x y, 7 m and 11 d SOL_PR_2.05_06

 YEARS NET CASH FLOWS 1 200,000 2 240,000 3 260,000 4 260,000

Determine if it is interesting to make the investment according to the Payback and according to the Net Present Value, given an interest rate of 5%. Explain the economic meaning.

PR_2.06_06.- Order the following projects of investment (from best to worst) according to the criteria of Net Present Value, being the annual interest rate 7% and indicating whin ones are viable. OUTCOMES: NPVX = 47,546.43; NPVY = 41,673.84; NPVZ = 43,018.64 SOL_PR_2.06_06

 Projects of investment A Q1 Q2 Q3 Q4 X 22,000 8,500 17,000 25,500 34,000 Y 31,000 7,300 17,300 27,300 37,300 Z 31,500 22,000 22,000 22,000 22,000

PR_2.01_07.- The firm Valpe, Ltd. has three projects of investment, that mean an outlay and ones net cash flows that appear in the following table: OUTCOMES: NPVX = 36,724.12; NPVY = 24,474.1; NPVZ = 12,962.03; PBX = x y, 4 m and 9 d; PBY = x y and 6 m; PBZ = x y, 8 m and 19 d SOL_PR_2.01_07

 Projects of investment Initial outlay INPUTS 1st year 2nd year 3rd year 4th year X 20,000 15,000 14,000 20,000 12,000 Y 23,500 14,000 19,000 18,000 -- Z 14,000 13,000 - 10,500 16,000 10,800

Calculate the more profitable investment, if the interest rate is 3%, according to the methods of Net Present Value and the Payback of each one of them

PR_2.02_07.- A project of investment had an initial outlay of 200,000€ and the cash flows of the first and the second year were, 80,000€ and 60,000€ respectively. Calculate the cash flow of the third year knowing that the Payback of the investment was two years and nine months. OUTCOME: X = 80,000€ SOL_PR_2.02_07

PR_2.03_07.- The firm “GOLDFINCH, Ltd”, is planning to make a new investment and it has several options: option A and option B. In the following table appear all the data related to the investment in euros. The initial outlay of both investments is 90,000€ and the interest rate is 5%. OUTCOMES: NPVA = 26,682.87; NPVB = 29,771.08; PBA = x y and 4 m; PBB = x y, 7 m and 6 d SOL_PR_2.03_07

 OPTION A OPTION B COLLECTIONS PAYMENTS COLLECTIONS PAYMENTS 1st year 80,000 50,000 180,000 120,000 2nd year 140,000 100,000 180,000 130,000 3rd year 150,000 90,000 180,000 160,000

1. Use the criteria of Net Present Value and Payback.

2. Which option is the best according to each one of the criteria and why

PR_2.04_07.- The firm of cans of vegetable Vegetalinea, Ltd., wants to expand its installed capacity to the canning of its products. In order to that it has selected three alternatives. The expected cash flows in the next four years for each one of the projects of investment are the following: OUTCOMES: NPV1 = 4,169.74; NPV2 = 2,119.51; NPV3 = -2,226.21; PB1 = x y and 2 m; PB2 = x y, 1 m and 10 d; PB3 = x y, 5 m and 20 d SOL_PR_2.04_07

 1st year 2nd year 3rd year 4th year 1st alternative -500 2,000 3,000 3,200 2nd alternative -1,000 2,300 3,200 4,500 3rd alternative -2,000 -500 4,000 5,000

The needed investments are 2,000, 5,000 and 7,000 monetary unities, respectively, for the 1st, 2nd and 3rd alternatives. The planned interest rate is 7%.

Determine the best alternative for the firm by using the following methods:

1. The Payback

2. The Net Present Value.

PR_2.01_08.- The firm plans to make a new investment. In order to that it has the two following possibilities: OUTCOMES: NPVA = 3,971.87; NPVB = 1,456.21 SOL_PR_2.01_08

Year

Project A

Project B

Collections

Payments

Collections

Payments

0

0

3,000

0

2,000

1

2,000

1,000

3,000

4,000

2

5,000

2,000

5,000

1,000

3

6,000

2,000

3,000

2,000

1. Calculate the cash flows of each period

2. Select the preferable investment, according to the criteria of NPV, if the interest rate is 6%

PR_2.02_08.- The data related to two projects of investment that a firm wants to evaluate are in the attached table: OUTCOMES: NPVA = 5,768.35; NPVB = 3,558.56; PBA = x y and 8 m; PBB = x y, 10 m and 15 d SOL_PR_2.02_08

Project

Initial outlay

Cash flow 1st year

Cash flow 2nd year

Cash flow 3rd year

Cash flow 4th year

Cash flow 5th year

A

10,000

0

0

6,000

6,000

8,000

B

16,000

4,000

5,000

8,000

3,000

3,000

If the annual interest rate is 6%.

1. Put in order the investments according to the criteria of Net Present Value (NPV)

2. Put in order the investments according to the criteria of Payback. Consider that the cash flows are obtained in an uniform way along the year.

3. Comment the outcomes

PR_2.03_08.- A firm is studying two projects of investment: Italica and Betica. The project Italica means an initial outlay of 120,000€ and it's expected to obtain, in each one of the five years, a net cash flow of 36,000€. The project Betica also means an initial outlay of 120,000€, but the net cash flows expected during the five years of life of the project are: 18,000€ 1st year, 30,000€ 2nd year, 54,000€ 3rd year, 48,000€ 4th year and 43,000€ 5th year. Being the interest rate 6%, determine which of the two investments is the best according to the NPV method. OUTCOMES: NPVI = 31,645.08; NPVB = 39,173.06 SOL_PR_2.03_08

PR_2.04_08.- The firm X produces and sells chocolates. As the business works very well in Spain and it has available money, it's thinking about to expand to Poland, building there a new factory. The investment lasts 4 years, being the net cash flow of the 1st year 120,000€, 132,000€ 2nd year, 145,000€ 3rd year and 160,000 4th year. The initial outlay is 290,000€ and the interest rate is 6% OUTCOMES: NPV = 189,166.87; PB = x y, 3 m and 4 d SOL_PR_2.04_08

Calculate:

1. The Net Present Value of the investment

2. The Payback. Consider that the cash flow are obtained in an uniform way along the year

3. Explain the economic meaning of the obtained outcomes

PR_2.05_08.- A businessman is thinking about to make an investment to expand his facilities, in order to that he must pay 15,000€ in the initial moment. The collections are 8,100€ 1st year and 12,000€ the following years. The payments are 4,500€ 1st year and 5,400€ the rest of the years. If the useful life is 6 years and the annual interest rate is 6%, obtain the NPV of the investment and the Payback OUTCOMES: NPV = 14,624.16; PB = x y, 8 m and 22 d SOL_PR_2.05_08

PR_2.06_08.- A firm is thinking about the two following possible projects of investment: OUTCOMES: NPVA = 2,870.02; NPVB = 3,073.63 SOL_PR_2.06_08

Initial outlay

Cash flow 1st year

Cash flow 2nd year

Cash flow 3rd year

Project A

10,000

3,000

5,000

8,000

Project B

9,000

7,000

6,000

1,000

Determine which is the best option according to the net present value. The interest rate is 10%. Explain the economic meaning of the obtained outcomes

PR_2.01_09.- We have a project of investment with the follwing data:

R0 = 80 m.u. F1 = 70 m.u. F2 = 30 m.u. F3 = 30 m.u.

The interest rate is 30%; we want to know:

1. The net present value

2. Is it acceptable the investment?

OUTCOME: NPV = 5.25 SOL_PR_2.01_09

PR_2.02_09.- A firm is thinking about the following two projects of investment: RESULTADOS : VANA = 96,34; VANB = 110,53 SOL_PR_2.02_09

Project

Initial outlay

Cash flow 1st year

Cash flow 2nd year

Cash flow 3rd year

Cash flow 4th year

A

500

100

0

400

300

B

600

300

100

200

300

1. Determine the net present value of each one of the projects of investment. The interest rate is 10%

2. Which is the best option and why?

PR_2.03_09.- The firm “2nd year of high school degree, Ltd” sells chemical products and it's thinking to expand its business to the sale of plant health products to the agriculture. In order to that it has the possibility of make the following two projects : OUTCOMES: PB1 = x y, PB2 = x y; NPV1 = 2,446.22; NPV2 = 862.65 SOL_PR_2.03_09

1st year

2nd year

3rd year

Collections

Payments

Collections

Payments

Collections

Payments

Project 1

600€

750€

2,200€

350€

3,800€

400€

Project 2

4,000€

3,000€

5,000€

4,000€

6,000€

5,900€

Determine the more profitable project knowing that the project 1 has an initial outlay of 1,700 and the project 2 another of 1,000€

1. According to the criteria of Payback

2. According to the net present value. The interest rate is 8%

PR_2.04_09.- Given the two projects of investment which initial outlays and cash flows are in the following table: OUTCOMES: PBA = x y; PBB = x y; NPVA = - 323.87; NPVB = 8,628.84 SOL_PR_2.04_09

Cash flows (m.u.)

Projects

1st year

2nd year

3rd year

4th year

Initial outlays

A

400

3,600

100

100

4,000

B

800

2,000

1,200

12,000

4,000

1. Which is the best investment according to the Payback?

2. Which is the net present value of each one of the projects. The interest rate is 7%

PR_2.05_09.- A catering industry firm, wants to make an investment and needs to value the best according to the criteria of the net present value. The interest rate is 4%. Which is the best options? (Quantities in euros) OUTCOMES : NPVA = 1,715.6; NPVB = - 253.3; NPVC = 2,011.13; PBA = x y and 6 m; PBB = x y and 7m; PBC = x y and 9 m SOL_PR_2.05_09

Investment

Initial outlay

F1

F2

F3

A

1,600

1,000

1,200

1,400

B

2,000

500

600

800

C

2,400

1,200

1,600

2,000

Which would be the best option if the used method is the Payback?

SOLUTIONS TO THE PROBLEMS OF 3rd PART TOPIC 9.-

SOL_PR_2.01_03.-

NPVX = -18,000 + 7,000 : 1.07 + 9,000 : 1.072 + 8,000 : 1.073 + 12,000 : 1.074

NPVX = -18,000 + 6,542.06 + 7,860.95 + 6,530.38 + 9,154.74 = 12,088.13€

NPVY = -30,000 + 15,000 : 1.07 + 15,000 : 1.072 + 15,000 : 1.073

NPVY = -30,000 + 14,018.69 + 13,101.58 + 12,244.47 = 9,364.74€

NPVZ = -25,000 + 12,000 : 1.07 + 11,000 : 1.072 + 10,000 : 1.073

NPVZ = -25,000 + 11,214.95 + 9,607.83 + 8,162.98 = 3,985.75€

According to this method the best investment is the investment X because it obtains more profit than the others

SOL_PR_2.02_03.-

NPV = - 600,000 + 50,000 : 1.08 + 140,000 : 1.082 + 235,000 : 1.083 + 235,000 : 1.084

NPV = - 600,000 + 46,296.296 + 120,027.434 + 186,550.576 + 172,732.015 = -74,393.679€

According to this method this investment wouldn't be interesting to the firm because it's lossing money

The Payback is more than 3 years. We are going to calculate the months:

235,000 ----- 12 months

175,000 ------ x months

x = (175,000 x 12) : 235,000 = 8.94 months. We are going to calculate the dates:

1 month ------------- 30 days

0.94 monts ------------ x days

x= 0.94 x 30 = 28 days. The payback is 3 years, 8 months and 28 days

According to this method this investment would be interesting to the firm because it recovers the initial outlay before the planned five years

SOL_PR_2.03_03.-

Raw material rotation = 977,000,000 : 63,000,000 = 15.51

Raw material conversion period = 365 : 15.51 = 23.53 days

Good in process rotation = 2,104,000,000 : 48,000,000 = 43.83

Good in process conversion period = 365 : 43.83 = 8.33 days

Finished goods rotation = 2,012,000,000 : 115,000,000 = 17.50

Finished goods conversion period = 365 : 17.50 = 20.86 days

Payment from customers rotation = 2,415,000,000 : 138,000,000 = 17.5

Receivables conversion period = 365 : 17.5 = 20.86

Cash conversion cycle = 23.53 + 8.33 + 20.86 + 20.86 = 73.58

This firm takes 74 days to realize the full operating cycle; being this the period of time that the firm takes to recover the investments in current assets that it needs to do the aforementioned cycle

SOL_PR_2.04_03.-

NPVA = - 1,000,000 + 100,000 : 1.07 + 150,000 : 1.072 + 200,000 : 1.073 + 250,000 : 1.074 + 300,000 : 1,075 = - 207,647€

NPVB = - 1,500,000 + 200,000 : 1.07 + 300,000 : 1.072 + 350,000 : 1.073 + 400,000 : 1.074 + 500,000 : 1.075 = - 103,697€

NPVC = - 1,700,000 + 400,000 : 1.07 + 600,000 : 1.072 + 300,000 : 1.073 + 600,000 : 1.074 + 400,000 : 1.075 = 185.716€

The best investment is project C because it's the only one with a positive NPV

SOL_PR_2.05_03.-

a)

a.1)

NPVA = - 10,000,000 + 6,000,000 : 1.063 + 6,000,000 : 1.064 + 8,000,000 : 1.065 = 5,768,343.06

NPVB = - 20,000,000 + 3,000,000 : 1.06 + 4,000,000 : 1.062 + 5,000,000 : 1.063 + 6,000,000 : 1.064 + 8,000,000 : 1.065 = 1,318,898.21

NPVC = -16,000,000 + 4,000,000 : 1.06 + 5,000,000 : 1.062 + 8,000,000 : 1.063 + 3,000,000 : 1.064 + 3,000,000 : 1.065 = 3,558,576.88

According to this criteria the best project would be project A, the second best project would be project C and the last one would be project B

a.2)

The Payback of project A will be more than 3 years. We are going to calculate the months:

6,000,000 ------- 12 months

4,000,000 ------- x months

x = (4,000,000 x 12) : 6,000,000 = 8 months

The Payback of project A will be 3 years and 8 months

The Payback of project B will be more than 4 years. We are going to calculate the months:

8,000,000 -------- 12 months

2,000,000 -------- x months

x = (2,000,000 x 12) : 8,000,000 = 3 months

The Payback of project B will be 4 years and 3 months

The Payback of project C will be more than 2 years. We are going to calculate the months

8,000,000 ------ 12 months

7,000,000 ------ x monts

x = (7,000,000 x 12) : 8,000,000 = 10.5 months. We are going to calculate the days

1 month -------- 30 days

0,5 months --------- x days

x = 0.5 x 30 = 15 days

The Payback of project C will be 2 years, 10 months and 15 days

According to this criteria the best project would be project C, the second best project would be project A and the last one would be project B

b) The NPV shows us the quantity that we earned if we would move all the collections and the payments to the current moment; the hight profit the best investment

The Payback calculates the period of time to recover the initial outlay; the least time the best investment

SOL_PR_2.06_03.-

NPVA = -10,000,000 + 1,000,000 : 1.08 – 2,000,000 : 1.082 + 6,000,000 : 1.083 + 6,000,000 : 1.084 + 8,000,000 : 1.085 = 3,829,086.43

NPVB = -18,000,000 – 3,000,000 : 1.08 + 4,000,000 : 1.082 + 5,000,000 : 1.083 + 6,000,000 : 1.084 + 8,000,000 : 1.085 = -3,524,416.59

NPVC = -16,000,000 + 4,000,000 : 1.08 + 5,000,000 : 1.082 + 8,000,000 : 1.083 + 3,000,000 : 1.084 + 3,000,000 : 1.085 = 2,587,894.88

According to this criteria the best project would be project A, the second best project would be project C and the last one would be project B

The Payback of A is more than 3 years. We are going to calculate the months

6,000,000 ------- 12 months

5,000,000 ------- x months

x = (5,000,000 x 12) : 6,000,000 = 10 months

The Payback is 3 years and 10 months

The Payback of B is more than 4 years. We are going to calculate the months

8,000,000 ------- 12 months

6,000,000 ------- x months

x = 9 months

The Payback of B is 4 years and 9 months

The Payback of C is more than 2 years. We are going to calculate the months

8,000,000 ------- 12 months

7,000,000 ------- x months

x = 10.5 months. We are going to calculate the days

1 month -------- 30 days

0.5months ------- x days

x = 0.5 x 30 = 15 days

The Payback of C is 2 years, 10 months and 15 days

According to the Payback the best project is project C, the second best project is project A and the last one es project B

SOL_PR_2.07_03.-

PBA = 2 years

PBB = 3 years

Therefore, the best investment, according to the Payback is the investment A

NPVA = -10,000 + 5,000 : 1.1 + 5,000 : 1.12 + 5,000 : 1.13 + 5,000 : 1.14 = 5,849.50

NPVB = -10,000 + 2,000 : 1.1 + 4,000 : 1.12 + 4,000 : 1.13 + 20,000 : 1.14 = 11,789.50

Therefore, the best investment according to the NPV is the investment B because it has the highest NPV

There isn't an agreement between both criteria because according to the Payback teh best investment is investment A and according to the NPV, the best investment is investment B

The NPV shows us the quantity that we earned if we would move all the collections and the payments to the current moment; the hight profit the best investment

The Payback calculates the period of time to recover the initial outlay; the least time the best investment

SOL_PR_2.08_03.-

NPVA = -10,000 + 2,000 : 1.1 + 6,000 : 1.12 + 8,000 : 1.13 = 2,787.37

NPVB = - 8,000 + 3,000 : 1.1 + 5,000 : 1.12 + 3,000 : 1.13 = 1,113.44

According to this criteria the best investment is investment A because it has a higher NPV

The Payback of A is more than 2 years. We are going to calculate the months

8,000 ------- 12 months

2,000 ------- x months x = 3 months

The Payback of A is 2 years and 3 months

The Payback of B is 2 years

According to this criteria the best investment is investment B because we recover the initial outlay before than in the other investment

There isn't an agreement between both criteria because according to the Payback the best investment is B and according to the NPV the best investment is A

The NPV shows us the quantity that we earned if we would move all the collections and the payments to the current moment; the hight profit the best investment

The Payback calculates the period of time to recover the initial outlay; the least time the best investment

SOL_PR_2.09_03.-

Nominal value = 73,647 : 4,900 = 15.03 €/share

Market value = 15.03 x 1.65 = 24.80 €/share

Theoretical value = 2.40/0.07 = 34.29 €/share

SOL_PR_2.10 _03.-

NPVD = - 90,000 – 10,000 : 1.07 + 40,000 : 1.072 + 60,000 : 1.073 = -15,430.37€

NPVE = - 78,000 + 60,000 : 1.07 + 60,000 : 1,072 + 60,000 : 1,073 = 79,458.96€

According to this criteria, the expansion is the best option

The Payback of the diversification is 3 years

The Payback of the expansion is more than 1 year. We are going to calculate the months

60,000 ------ 12 months

18,000 ------ x months x = 3.6 months. We are going to calculate the days

1 month --------- 30 days

0.6 months ------- x days x = 18 days

The Payback of the expansion is 1 year, 3 months and 18 days

According to this criteria, the firm would opt for the expansion, as well

SOL_PR_2.11_03.-

x ---------- 12 months

30,000 ----------- 9 months x = 40,000€

SOL_PR_2.12_03.-

Nominal value = 120,000 : 300 = 400€

Theoretical value = (120,000 + 24,000) : 300 = 480€

Distributing dividend per share = 12,000 : 300 = 40€

Net worth = 120,000 + 24,000 = 144,000€

SOL_PR_2.13_03.-

NPV = -1,500 + 300 : 1.05 + 300 : 1.052 + 500 : 1.053 + 500 : 1.054 + 500 : 1.055 = 292.85 m.u.

SOL_PR_2.14_03.-

NPVA = -25,000 + 30,000 : 1.0653 + 12,000 : 1.0654 = 9,163.35€

NPVB = -20,000 – 5,000 : 1.065 – 2,000 : 1.0652 + 15,000 : 1.0653 + 15,000 : 1.0654 = -2,380.57€

NPVC = -16,000 + 5,000 : 1.065 + 6,000 : 1.0652 + 7,000 : 10653 + 8,000 : 1.0654 = 5,998.32€

According to this criteria the best project is project A, the second best project is project C and the last one is project B

The Payback of A is more than 2 years. We are going to calculate the months

30,000 ------ 12 months

25,000 ------ x months x = 10 months

The Paybak of A es 2 years and 10 months

The Payback of B is more than 3 years. We are going to calculate the months

15,000 ------ 12 months

12,000 ------ x months x = 9.6 months. We are going to calculate the days

1 month -------------------- 30 days

0.6 months --------- x days x = 18 days

The Payback of B is 3 years, 9 months and 18 days

The Payback of C is more than 2 years. We are going to calculate the months

7,000 ---------- 12 months

5,000 ---------- x months x = 8.57 months. We are going to calculate the days

1 month -------------- 30 days

0.57 months ------- x days x = 17 days

The Payback of C is 2 years, 8 months and 17 days

According to this criteria the best is C, the second is A and the last one is B

SOL_PR_2.15_03.-

NPVA = -1,000,000 + 300,000 : 1.05 + 300,000 : 1.052 + 300,000 : 1.053 + 300,000 : 1.054 + 300,000 : 1.055 = 298,843€

NPVB = -1,000,000 + 150,000 : 1.05 + 250,000 : 1.052 + 450,000 : 1.053 + 400,000 : 1.054 + 350,000 : 1.055 = 361,656.58€

According to this criteria, project B is the best option because the NPV is the highest

SOL_PR_2.16_03.-

REPETIDO

SOL_PR_2.17_03.-

Igual que 2.12_03

SOL_PR_2.18_03.-

NPVA = -10,000 + 2,000 : 1.08 + 2,500 : 1.082 + 3,000 : 1.083 + 3,000 : 1.084 + 3,100 : 1.085 = 691.6€

NPVB = -14,100 + 3,000 : 1.08 + 3,400 : 1.082 + 3,200 : 1.083 + 3,000 : 1.084 + 3,000 : 1.085 = -1,620.17€

According to the NPV method, project a is preferable to project B

The Payback of project A is more than 3 years. We are going to calculate the months

3,000 ------- 12 months

2,500 ------- x months x = 10 months

The Payback of project A is 3 years and 10 months

The Payback of project B is more than 4 years. We are going to calculate the months

3,000 -------- 12 months

1,500 -------- x months x = 6 months

The Payback of project B is 4 years and 6 months.

According to this criteria, project A is preferable to project B

SOL_PR_2.19_03.-

Share Capital = 50,000 x 1,000 = 50,000,000 m.u.

The shares quote above par

Theoretical value of each share = (50,000,000 + 10,000,000) : 50,000 = 1,200 m.u.

SOL_PR_2.01_04.-

600 - - - - - - 12

500 - - - - - - x x = 10 m Payback of investment 1 = 1 year and 10 months

10,000 - - - - - - - - 12

400 - - - - - - - - - - - x x = 0.48

1 month - - - - - - - - - 30 days

0.48 months - - - - - -- x days x = 14 days Payback of investment 2 = 2 years and 14 days

According to the Payback, investment 1 is preferable to investment 2

Investment 2 is more profitable because, although we take more time, we get far more money

SOL_PR_2.02_04.-

Cash flows year 0 (before taxes) = - 13,000

Cash flows 1st year (before taxes) = 6,000 – 1,050

Cash flows 2nd year (before taxes) = 12,000 – 1,130

Cash flows 3rd year (before taxes) = 12,500 – 1,350

Cash flows 4th year (before taxes) = 20,000 – 1,350

Taxes 1st year = (6,000 – 1,050) x 0.25 = 1,237.5

Taxes 2nd year = (12,000 – 1,130) x 0.25 = 2,717.5

Taxes 3rd year = (12,500 – 1,350) x 0.25 = 2,787.5

Taxes 4th year = (20,000 – 1,350) x 0.25 = 4,662.5

Cash flows year 0 (after taxes) = - 13,000

Cash flows 1st year (after taxes) = 6,000 – 1,050 – 1,237.5 = 3,712.5

Cash flows 2nd year (after taxes) = 12,000 – 1,130 – 2,717,5 = 8,152.5

Cash flows 3rd year (after taxes) = 12,500 – 1,350 – 2,787.5 = 8,362.5

Cash flows 4th year (after taxes) = 20,000 – 1,350 – 4,662.5 = 13,987.5

NPV = - 13,000 + (3,712.5 : 1.15) + (8,152.5 : 1.152) + (8,362.5 : 1.153) + (13,987.5 : 1.154) = 9,888.6 The investment is a good idea for the firm

SOL_PR_2.03_04.-

NPV = - 3,000 + (1,000 : 1.05) + (1,000 : 1.052) + (1,000 : 1.053) + (1,200 : 1.054) = 710.49€

SOL_PR_2.01_05.-

NPVX = - 11,000 + (8,000 : 1.04) + (10,000 : 1.042)+ (12,000 : 1.043) =

NPVX = - 11,000 + 7,692.31 + 9,245.56 + 10,667.96 = 16,605.83

NPVY = - 11,000 + (10,000 : 1.04) + (10,000 : 1.042) + (10,000 : 1.043) =

NPVY = - 11,000 + 9,615.38 + 9,245.56 + 8,889.96 = 16,750.9

The investment X is more interesting than investment Y because X has the highest NPV

SOL_PR_2.02_05.-

NPVA = - 10,000 + (7,500 : 1.08) + (3,600 : 1.082) + (500 : 1.083) =

NPVA = - 10,000 + 6,944.44 + 3,086.42 + 396.92 = 427.78

NPVB = - 10,000 + (4,000 : 1.08) + (4,000 : 1.082) + (4.000 : 1.083) =

NPVB = - 10,000 + 3,703.70 + 3,429.36 + 3,175.33 = 308.39

NPVC = - 10,000 + (8,000 : 1.082) + (3,000 : 1.083) =

NPVC = - 10,000 + 6,858.71 + 2,381.50 = - 759.79

According to this criteria, the best project is project A because it has the highest NPV

X = (2,500 x 12) : 3,600 = 8.33 m. __________ X = 0.33 x 30 = 9.9 d. ____ PBA = 1 y, 8 m and 10 d.

X = (2,000 x 12) : 4,000 = 6 m. _______ PBB = 2 y and 6 m.

X = (2,000 x 12) : 3,000 = 8 m. ________ PBC = 2 y and 8 m.

According to this criteria, the best project is project A because it has the least Payback

SOL_PR_2.03_05.-

X = (30,000 x 12) : 45,000 = 8 m. _______ PB1 = 2 y and 8 m

X = (38,000 x 12) : 52,000 = 8.77 m. ______ X = 0.77 x 30 = 23.1 d. _____ PB2 = 2 y, 8 m and 23 d

X = (40,000 x 12) : 55,000 = 8.73 m. ______ X = 0.73 x 30 = 21.9 d. _____ PB3 = 2 y, 8 m and 22 d

According to this criteria, the best option is project 1

NPV1 = - 80,000 + (50,000 : 1.0452) + (45,000 : 1.0453)

NPV1 = - 80,000 + 45,786.50 + 39,433.35 = 5,219.85

NPV2 = - 90,000 + (52,000 : 1.045) + (52,000 : 1.0453)

NPV2 = - 90,000 + 49,760.77 + 45,567.42 = 5,328.19

NPV3 = - 80,000 + (40,000 : 1.045) + (55,000 : 1.0453)

NPV3 = - 80,000 + 38,277.51 + 48,196.31 = 6,473.82

According to this criteria, the best option is project 3

SOL_PR_2.04_05.-

X = (5,000 x 12) : 8,000 = 7.5 m ____ X = 0.5 x 30 = 15 d _____ PBA = 2 y, 7m and 15 d

X = (19,000 x 12) : 20,000 = 11.4 m _____ X = 0.4 x 30 = 12 d _______ PBB = 3 y, 11 m and 12 d

X = (13,000 x 12) : 14,000 = 11.14 m ______ X = 0.14 x 30 = 4.2 d _____ PBC = 2 y, 11 m. and 4 d

According to the Payback the best option is investment A because it has the least Payback. I agree with the chief financial officer because investment A is the option that is recovered before and it's the option that more money recovers

SOL_PR_2.05_05.-

NPVA = - 20,000 + (10,000 : 1.04) + (8,000 : 1.042) + (20,000 : 1.043) + (4,000 : 1.044)

NPVA = - 20,000 + 9,615.38 + 7,396.45 + 17,779.93 + 3,419.22 = 18,210.98

NPVB = - 27,000 + (8.000 : 1.04) + (18,000 : 1.042)+ (16,000 : 1.043)

NPVB = - 27,000 + 7,692.31 + 16,642.01 + 14,223.94 = 11,558.26

NPVC = - 8,000 + (6,000 : 1.04) – (1,000 : 1.042) + (12,000 : 1.043) + (1,600 : 1.044)

NPVC = - 8,000 + 5,769.23 – 924.23 + 10,667.96 + 1,367.69 = 8,880.32

According to this criteria the order would be: A – B - C

X = (2,000 x 12) : 20,000 = 1.2 m _____ X = 0.2 x 30 = 6 d ____ PBA = 2 y, 1 m and 6 d

X = (1,000 x 12) : 16,000 = 0.75 m _____ X = 0.75 x 30 = 22.5 d ___ PBB = 2 y and 23 d

X = (3,000 x 12) : 12,000 = 3 m ______ PBC = 2 y and 3 m

According to this criteria the order would be: B – A - C

SOL_PR_2.06_05.-

X = (4,000 x 12) : 5,000 = 9.6 m _____ X = 0.6 x 30 = 18 d ____ PBA = 1 y, 9 m. and 18 d

x = (5,000 x 12) : 20,000 = 3 m ______ PBB = 2 y and 3 m

According to this criteria the best option is investment A because we recover it before than investment B

NPVA = - 10,000 + (6,000 : 1.06) + (5,000 : 1.062) + (100 : 1.063)

NPVA = - 10,000 + 5,660.38 + 4,449.98 + 83.96 = 194.32

NPVB = - 10,000 + (1,000 : 1.06) + (4.000 : 1.062) + (20.000 : 1.063)

NPVB = - 10,000 + 943.40 + 3,559.99 + 16,792.39 = 11,295.78

According to this criteria the best option is investment B

The two methods don't coincide to indicate which investment is the best because the Payback looks for which investment is recovered before and the NPV looks for which investment is going to reach a highest profit. The best criteria is the NPV.

SOL_PR_2.01_06.-

NPVA = - 800 – (50 : 1.1) + (150 : 1.12) + (250 : 1.13) + (350 : 1.14) + (450 : 1.15)

NPVA = - 800 – 45.45 + 123.97 + 187.83 + 239.05 + 279.41 = - 15.19

NPVB = - 950 + (100 : 1.1) + (200 : 1.12) + (300 : 1.13) + (350 : 1.14) + (500 : 1.15)

NPVB = - 950 + 90.91 + 165.29 + 225.39 + 239.05 + 310.46 = 81.1

NPVC = - 750 – (50 : 1.1) + (100 : 1.12) + (400 : 1.13) + (300 : 1.14) + (200 : 1.15)

NPVC = - 750 – 45.45 + 82.64 + 300.53 + 204.90 + 124.18 = - 83.2

According to this criteria the only one interesting option is investment B, because the others are negative; the order would be: B – A - C

X = (100 x 12) : 450 = 2.67 months

X = (0.67 x 30) : 1 = 20.1 days

PBA = 4 y, 2 m and 20 d

PBB = 4 years

PBC = 4 years

According to this criteria, investments B and C would be in the first place and investment A in the last place

SOL_PR_2.02_06.-

NPV1 = - 180,000 + (100,000 : 1.052) + (100,000 : 1.053) = - 180,000 + 90,702.95 + 86,383.76

NPV1 = - 2,913.29

NPV2 = - 190,000 + (70,000 : 1.05) + (70,000 : 1.052) + (70,000 : 1.053)

NPV2 = - 190,000 + 66,666.67 + 63,492.06 + 60,468.63 = 627.36

NPV3 = - 160,000 + (110,000 : 1.05) + (80,000 : 1.053) = - 160,000 + 104,761.90 + 69,107.01

NPV3 = 13,868.91

According to this criteria the best option is investment 3 because it has the highest NPV

X = (80,000 x 12) : 100,000 = 9.6 months

X = (0.6 x 30) : 1 = 18 days

PB1 = 2 years, 9 months and 18 days

X = (50,000 x 12) : 70,000 = 8.57 months

X = (0.57 x 30) : 1 = 17.1 days

PB2 = 2 years, 8 months and 17 days

X = (50,000 x 12) : 80,000 = 7.5 months

X = (0.5 x 30) : 1 = 15 days

PB3 = 2 years, 7 months and 15 days

According to this criteria the best option is investment 3 because it is recovered before than the others

SOL_PR_2.03_06.-

NPV = - 1,500 + (300 : 1.06) + (300 : 1.062) + (500 : 1.063) + (500 : 1.064) + (500 : 1.065)

NPV = - 1,500 + 283.02 + 267.00 + 419.81 + 396.05 + 373.63 = 239.51

X = (400 x 12) : 500 = 9.6 months

X = (0.6 x 30) : 1 = 18 days

PB = 3 years, 9 months and 18 days

SOL_PR_2.04_06.-

NPV1 = - 5,000 + (3,000 : 1.052) + (3,000 : 1.053) = - 5,000 + 2,721.09 + 2,591.51 = 312.6

NPV2 = - 5,000 + (1,000 : 1.05) + (4,800 : 1.053) = - 5,000 + 952.38 + 4,146.42 = 98.8

According to this criteria the best option would be investment 1 because it has the highest NPV

X = (2,000 x 12) : 3,000 = 8 months

PB1 = 2 years and 8 months

X = (4,000 x 12) : 4,800 = 10 months

PB2 = 2 years and 10 months

Accordign to this criteria the best option would be project a because it has the least Payback

SOL_PR_2.05_06.-

NPV = - 600,000 + (200,000 : 1.05) + (240,000 : 1.052) + (260,000 : 1.053) + (260,000 : 1.054)

NPV = - 600,000 + 190,476.19 + 217,687.07 + 224,597.78 + 213,902.26 = 246,663.3

According to this criteria would be interesting to make the investment because it has a positive NPV

X = (160.000 x 12) : 260.000 = 7,38 months

X = (0,38 x 30) : 1 = 11,4 days

PB = 2 years, 7 months y 11 days

Según este criterio no podemos decir si interesa o no realizarla ya que no se nos ha dado un plazo máximo de recuperación

SOL_PR_2.06_06.-

NPVX = - 22,000 + (8,500 : 1.07) + (17,000 : 1.072) + (25,500 : 1.073) + (34,000 : 1.074)

NPVX = - 22,000 + 7,943.93 + 14,848.46 + 20,815.60 + 25,938.44 = 47,546.43

NPVY = - 31,000 + (7,300 : 1.07) + (17,300 : 1.072) + (27,300 : 1.073) + (37,300 : 1.074)

NPVY = - 31,000 + 6,822.43 + 15,110.49 + 22,284.93 + 28,455.99 = 41,673.84

NPVZ = - 31,500 + (22,000 : 1.07) + (22,000 : 1.072) + (22,000 : 1.073) + (22,000 : 1.074)

NPVZ = - 31,500 + 20,560.75 + 19,215.65 + 17,958.55 + 16,783.69 = 43,018.64

According to this criteria, from best to worts, the order would be: X – Z – Y. All the projects are viable because all of then are positive

SOL_PR_2.01_07.-

NPVX = - 20,000 + (15,000 : 1.03) + (14,000 : 1.032 )+ (20,000 : 1.033 )+ (12,000 : 1.034) = 36,724.12

NPVY = - 23,500 + (14,000 : 1.03) + (19,000 : 1.032) + (18,000 : 1.033) = 24,474.1

NPVZ = - 14,000 + (13,000 : 1.03) + (10,500 : 1.032) + (16,000 : 1.033) + (10,800 : 1.034) = 12,962.03

According to this criteria, the more profitable option is investment X because it has the highest NPV

PBX = 1 y, 4 m and 9 d x = (5,000 x 12) : 14,000 = 4.29 m x= 0.29 x 30 = 8.7 = 9 d

PBY = 1 y and 6 m x = (9,500 x 12) : 19,000 = 6 m

PBZ = 2 y, 8 m and 19 d x = (11,500 x 12) : 16,000 = 8.63 m x = 0.63 x 30 = 18.9 = 19 d

According to this criteria, the more profitable option is investment X because it recovers the initial outlay before than the others

SOL_PR_2.02_07.-

R3 = (60,000 x 12) : 9 = 80,000€

SOL_PR_2.03_07.-

NPVA = - 90,000 + (30,000 : 1.05) + (40,000 : 1.052) + (60,000 : 1.053) = 26,682.87€

NPVB = - 90,000 + (60,000 : 1.05) + (50,000 : 1.052) + (20,000 : 1.053) = 29,771.08€

According to this criteria, the best option is investment B because it has the highest NPV

PBA = 2 y and 4 m

X = (20,000 x 12) : 60,000 = 4 m

PBB = 1 y, 7 m and 6 d

X = (30,000 x 12) : 50,000 = 7.2 m x = 0.2 x 30 = 6 d

According to this criteria, the best option is investment B because it recovers the initial outlay before than the other

SOL_PR_2.04_07.-

NPV1 = - 2,000 – (500 : 1.07) + (2,000 : 1.072) + (3,000 : 1.073) + (3.200 : 1.074) = 4,169.74 m.u.

NPV2 = - 5,000 – (1,000 : 1.07) + (2,300 : 1.072) + (3,200 : 1.073) + (4,500 : 1.074) = 2,119.51 m.u.

NPV3 = - 7,000 – (2,000 : 1.07) – (500 : 1.072) + (4,000 : 1.073) + (5,000 : 1.074) = - 2,226.21 m.u.

According to this criteria, the best option is investment 1 because it has the highest NPV

PB1 = 2 y and 2 m

X = (500 x 12) : 3,000 = 2 m

PB2 = 3 y, 1 m and 10 d

X = (500 x 12) : 4,500 = 1.33 m x = 0.33 x 30 = 9.9 d = 10 d

PB3 = It isn't recovered

According to this criteria, the best option is investment 1, because it has the least Payback

SOL_PR_2.01_08.-

NPVa = - 3,000 + (1,000 : 1.06) + (3,000 : 1.062) + (4,000 : 1.063)

NPVa = - 3,000 + 943.40 + 2,669.99 + 3,358.48 = 3,971.87

NPVb = - 2,000 – (1,000 : 1.06) + (4,000 : 1.062) + (1,000 : 1.063)

NPVb = - 2,000 – 943.40 + 3,559.99 + 839.62 = 1,456.21

SOL_PR_2.02_08.-

NPVa = - 10,000 + (6,000 : 1.063) + (6,000 : 1.064) + (8,000 : 1.065)

NPVa = - 10,000 + 5,037.72 + 4,752.56 + 5,978.07 = 5,768.35

NPVb = - 16,000 + (4,000 : 1.06) + (5,000 : 1.062) + (8,000 : 1.063) + (3,000 : 1.064) + (3,000 : 1.065)

NPVb = - 16,000 + 3,773.58 + 4,449.98 + 6,716.95 + 2,376.28 + 2,241.77 = 3,558.56

SOL_PR_2.03_08.-

NPVi = - 120,000 + (36,000 : 1.06) + (36,000 : 1.062) + (36,000 : 1.063) + (36,000 : 1.064) + (36,000 : 1.065)

NPVi = - 120,000 + 33,962.26 + 32,039.87 + 30,226.29 + 28,515.37 + 26,901.29 = 31,645.08

NPVb = - 120,000 + (18,000 : 1.06) + (30,000 : 1.062) + (54,000 : 1.063) + (48,000 : 1.064) + (43,000 : 1.065)

NPVb = - 120,000 + 16,981.13 + 26,699.89 + 45,339.44 + 38,020.50 + 32,132.10 = 39,173.06

SOL_PR_2.04_08.-

NPV = - 290,000 + (120,000 : 1.06) + (132,000 : 1.062) + (145,000 : 1.063) + (160,000 : 1.064)

NPV = - 290,000 + 113,207.55 + 117,479.53 + 121,744.80 + 126,734.99 = 189,166.87

145,000 - - - - - - - 12m

38,000 - - - - - - - - x

x = 3.14 m

1m - - - - - - - - 30d

0.14m - - - - - - x

x = 4.2 d

PB = 2 y, 3 m and 4 d

SOL_PR_2.05_08.-

NPV = - 15,000 + (3,600 : 1.06) + (6,600 : 1.062) + (6,600 : 1.063) + (6,600 : 1.064) + (6,600 : 1.065) + (6,600 : 1.065)

NPV = - 15,000 + 3,396.23 + 5,873.98 + 5,541.49 + 5,227.82 + 4,931.90 + 4,652.74 = 14,624.16

6,600 - - - - - - - - 12m

4,800 - - - - - - - - x

x = 8.73m

1m - - - - - - - - - 30d

0.73m - - - - - - - x

x = 21.9 d

PB = 2 y, 8 m and 22 d

SOL_PR_ 2.06_08.-

NPVa = - 10,000 + (3,000 : 1.1) + (5,000 : 1.12) + (8,000 : 1.13)

NPVa = - 10,000 + 2,727.27 + 4,132.23 + 6,010.52 = 2,870.02

NPVb = - 9,000 + (7,000 : 1.1) + (6,000 : 1.12) + (1,000 : 1.13)

NPVb = - 9,000 + 6,363.64 + 4,958.68 + 751.31 = 3,073.63

SOL_PR_2.01_09.-

NPV = - 80 + (70 : 1.3) + (30 : 1.32) + (30 : 1.33) = - 80 + 53.85 + 17.75 + 13.65 = 5.25

It's acceptable because the NPV is positive

SOL_PR_2.02_09.-

NPVA = - 500 + (100 : 1.1) + (400 : 1.13) + (300 : 1.14)

NPVA = - 500 + 90.91 + 300.53 + 204.90 = 96.34

NPVB = - 600 + (300 : 1.1) + (100 : 1.12) + (200 : 1.13) + (300 : 1.14)

NPVB = - 600 + 272.73 + 82.64 + 150.26 + 204.90 = 110.53

SOL_PR_2.03_09.-

PB1 = 2 y

PB2 = 1 y

NPV1 = - 1,700 – (150 : 1.08) + (1,850 : 1.082) + (3,400 : 1.083)

NPV1 = - 1,700 – 138.89 + 1,586.08 + 2,699.03 = 2,446.22

NPV2 = - 1,000 + (1,000 : 1.08) + (1,000 : 1.082) + (100 : 1.083)

NPV2 = - 1,000 + 925.93 + 857.34 + 79.38 = 862.65

SOL_PR_2.04_09.-

PBA = 2 y

PBB = 3 y

NPVA = - 4,000 + (400 : 1.07) + (3,600 : 1.072) + (100 : 1.073) + (100 : 1.074)

NPVA = - 4,000 + 373.83 + 3,144.38 + 81.63 + 76.29 = - 323.87

NPVB = - 4,000 + (800 : 1.07) + (2,000 : 1.072) + (1,200 : 1.073) + (12,000 : 1.074)

NPVB = - 4,000 + 747.66 + 1,746.88 + 979.56 + 9,154.74 = 8,628.84

SOL_PR_2.05_09.-

NPVA = - 1,600 + (1,000 : 1.04) + (1,200 : 1.042) + (1,400 : 1.043)

NPVA = - 1,600 + 961.54 + 1,109.47 + 1,244.59 = 1,715.6

NPVB = - 2,000 + (500 : 1.04) + (600 : 1.042) + (800 : 1.043)

NPVB = - 2,000 + 480.77 + 554.73 + 711.20 = - 253.3

NPVC = - 2,400 + (1,200 : 1.04) + (1,600 : 1.042) + (2,000 : 1.043)

NPVC = - 2,400 + 1,153.85 + 1,479.29 + 1,777.99 = 2,011.13

PBA = 1 y and y 6 m

PBB = It isn't recovered

PBC = 1 y and 9 m